Diego Simeone's men won 1-0 to book a final clash against Marseille, but Nadal's presence at the Wanda Metropolitano - wearing an Atletico shirt around his neck - raised eyebrows.
The Spaniard, set to begin his Madrid Open title defence on Tuesday, attended the game as a guest of Atletico's president Enrique Cerezo.
"Well, there is a problem with today's society, that to be a true supporter of one team, it seems that you have to be anti another team," Nadal told reporters. "I just support Real Madrid. I have a lot of friends that are from Atletico.
"They are playing in a competition in Europe against an English team. I just went there to support Atletico Madrid. They invited me. I just wanted to enjoy the day, to see a great football match.
"The [Atletico] president gave me a T-shirt as a gift. At night it was a little bit chilly, a little bit cold, and I just used it as a scarf. That's all.
"But it's always the same stuff. Maybe there's too much hypocrisy, or I would say you people in the media have to write too many things, so you have to explore some stupid things."